Have you tried to install silverstripe several times in the same folder? Somtimes I had this problem too - but when I deleted all the files and database tables and installed it again it was suddenly running.

Is the .htaccess file writeable? Unable to detect whether I can write to files. Please ensure /.htaccess is writable.
Is the mysite/ folder writeable? Unable to detect whether I can write to files. Please ensure /mysite is writable.
Is the tutorial/ folder writeable? Unable to detect whether I can write to files. Please ensure /tutorial is writable.
Is the assets/ folder writeable? Unable to detect whether I can write to files. Please ensure /assets is writable.

You may use your the FTP Client. Login on your server. Select the file or folder you want to edit. The FTP client should have a menu for "file attributes" (also called chmod attributes). Mostly yout have to set some checkboxes for "reading and writing" (or chmod 777). Activate all for each file. Try again the installing. Maybe this will work now.